I noticed that Cycles is capable of using cubic texture interpolation for image textures but there is nothing in the manual about it, and every tutorial I've seen only mentions it by saying to leave it on Linear most of the time. I've done a bit of research on image scaling with linear/cubic/sinc but I can find very little in the context of texture filtering. What I'm wondering is this. Are there specefic cases where Cubic might be more useful than linear or where cubic could cause artifacts? For example when using textures that are smaller or larger than they appear in screen space, what would the pros and cons of each interpolation mode be?
Let's look at what the two mean and create examples. Our example image will be this (enlarged) $2\times2$ pixel grid:
Linear: In spaces between other pixels, there is a linear gradient of the two mixing colors:
Cubic: In spaces between other pixels, there is a cubic (also called Ease) gradient between the two colors:
When we compare the linear and cubic interpolations, the eased one seems to "bleed" a little bit, creating a much smoother interpolation, but it doesn't leave the original lines as defined, so it will blur the image.
Let's look at it with a more complex image:
Essentially, Linear interpolation will hold to the original definition of the shapes in the image, but won't look as pretty. Cubic interpolation will look nicer and smoother, but that comes at the cost of image clarity, since the image will appear blurred.
Also, when I did (very) small test renders on my computer, Linear was milliseconds faster than Cubic.